In atmospheric sciences, measurements provided by remote-sensing instruments are crucial in observing the state of atmosphere. The associated uncertainties are important in nearly all data analyses.
Random uncertainties reported by satellite instruments are typically estimated by inversion algorithms (ex-ante). They can be incomplete due to simplified or incomplete modelling of atmospheric processes used in the retrievals, and thus validating random uncertainties is important. However, such validation of uncertainties (or their estimates from statistical analysis afterwards, i.e. ex-post) is not a trivial task, because atmospheric measurements are obtained from the ever-changing atmosphere.
This Thesis aims to explore the structure function method – an important approach in spatial statistics – and apply it to total ozone column measurements provided by the nadir-viewing satellite instrument TROPOMI. This method allows us to simultaneously perform validation of reported ex-ante random uncertainties and to explore of local-scale natural variability of atmospheric parameters.
Two-dimensional structure functions of total ozone column have been evaluated based on spatial separations in latitudinal and longitudinal directions over selected months and latitude bands. Our results have indicated that the ex-post random uncertainties estimated agree considerably well with the reported ex-ante random uncertainties, which are within 1-2 DU. Discrepancies between them are very small in general.
The morphology of ozone natural variability has also been illustrated: ozone variability is minimal in the tropics throughout the year, whereas in middle latitudes and polar regions they attain maxima in local spring and winter. In every scenario, the ozone structure functions are anisotropic with a stronger variability in the latitudinal direction, except at specific seasons in polar regions where isotropic behaviour is observed.
Our analysis has demonstrated that the structure function method is a remarkable and promising tool for validating random uncertainties and exploring natural variability. It has a high potential for applications in other remote sensing measurements and atmospheric model data.
